Occasionally I use my DSLR for shots of people indoor that requires flash. But most of the pictures turn out really bad because of the flash. Either the colors look strange and exaggerated with dark background or huge shadows forms behind people and objects.

Is there a trick to get decent results with a build-in flash when shooting indoor?

The other important thing with a remote flash is, that it's much more powerful than your onboard flash. That allows you to place it at a greater distance from the object which has two benefits:
1. The light fall-off at your subject is much softer than with the onboard-flash
2. The further the flash is away, the more it tends to illuminate the whole room and cast a more natural light by reflecting from the walls and the ceiling

Hey, here's an altnerative idea if you're not getting what you want with your flash - try some shots without the flash, perhaps at higher ISOs if the conditions are dark - maybe 800 or 1600 ISO. You'll get a completely different type of shot with natural lighting. These can often look great turned into black and white, so you also don't have to worry about any internal light colours.

I also find people tend to relax more if they think it's too dark for you to take a successful shot without a flash!

I often find the incandescent light in closed rooms quite "spotty". That makes it hard to shoot a decent portrait unless you take a tripod and arrange everything perfectly. An added challenge is that light at the ceiling, esp. spots often paint deep shadows on peoples faces...

But your remark about high-ISO brought another thought up! Use a tele-lens/zoom to single out the face you like to shoot and increase the ISO to say 800 (before it really starts to get too grainy). That way the light-fall-off is much less pronounced and you might also catch some ambient light in the room. Just try out how far you can get away from your subject at high ISO so that the built-in flash still delivers enough light.

Great tips, thanks a lot! I did some tests, and zooming close to objects does improve the picture. And I really liked the effect when using high ISO, I shot with both 800 and 1600 and the grain/noise actually gives a nice effect for those kind of pictures. To get the best results with 1600 I had to underexpose a bit so it didn't look so daylightish.

What i also discovered was that blocking some of the flash with a sheet of paper actually softened the light which also turned out nice. But then the white balance gets a bit complicated since its a mix of flash and tungsten light...

Have fun experimenting anyway, and remember you can always take a custom white balance reading from a white sheet of card if the colours are looking odd - or shoot in RAW and give yourself more flexibility to adjust WB later. Or have an easy life and convert to B&W!

The mix of flash and ambient light is exactly the prob, that only goes away, when you either
(1) convert to b&w
(2) use a color filter for your flash that tones it down to incasdescent light
(3) flood the room with enough flashlight to drown the ambient light out.

For me it feels funny to go to b&w, but converting some ig the portraits I made, it is even more shocking to go back to the color-version. It all looks so "overcolored" Option (2) is a bit problematic when you want to use your onboard flash, because than you have to build some filter of your own: a.f.a.i.k. there are no color-filters for onboard flash...
(3) has to be done carefully not to totally erase the natural room feeling